Final answer:
Astronauts on the International Space Station feel weightless because they are in a state of free-fall around the Earth. Despite the presence of gravity, they and the objects around them are falling at the same rate, creating the sensation of weightlessness.
Step-by-step explanation:
Astronauts on the International Space Station feel weightless because they are in a state of free-fall. Although there is gravity acting upon them, they are continuously falling around the Earth. This sensation of weightlessness is similar to passengers in an elevator with a broken cable or in an airplane without engines. In these situations, both the astronauts and objects are falling at the same rate, creating the illusion of weightlessness.